$g$ Factor of Lithiumlike Silicon: New Challenge to Bound-State QED

The recently established agreement between experiment and theory for the $g$ factors of lithiumlike silicon and calcium ions manifests the most stringent test of the many-electron bound-state quantum electrodynamics (QED) effects in the presence of a magnetic field. In this Letter, we present a significant simultaneous improvement of both theoretical $g_$\text{th}$ = 2.000,889,894,4,(34)$andexperimental$g_$\text{exp}$ = 2.000,889,888,45,(14)$valuesofthe$g$factoroflithiumlikesilicon$^{28}$Si$^{11+}$. The theoretical precision now is limited by the many-electron two-loop contributions of the bound-state QED. The experimental value is accurate enough to test these contributions on a few percent level.